Interest rate model with humped volatility under the real-world measure
Abstract
The purpose of this paper is to develop real-world modeling for interest rate volatility with a humped term structure. We consider humped volatility that can be parametrically characterized such that the Hull–White model is a special case. First, we analytically show estimation of the market price of risk with humped volatility. Then, using U.S. treasury yield data, we examine volatility fitting and estimate the market price of risk using the Heath–Jarrow–Morton model, Hull–White model, and humped volatility model. Comparison of the numerical results shows that the real-world humped volatility model is adequately developed.References
Agca S. The performance of alternative interest rate risk measures and immunization strategies under a Heath-Jarrow-Morton framework. Journal of Financial and Quantitative Analysis 2005; 40(3): 645-669. doi:10.1017/S0022109000001903
Board of Governors of the Federal Reserve System. Available from; http://www.federalreserve.gov/releases/h15/data.htm
Brace A, Gatarek D, Musiela M, The Market Model of Interest Rate Dynamics, Mathematical Finance 1997; 7:127–155. doi: 10.1111/1467-9965.00028
Dempster MAH, Medova EA, Villaverde M, Long-term interest rates and consol bond valuation, Journal of Asset Management 2010; 11: 113–135. doi: 10.1057/jam.2010.7
Heath D, Jarrow R, Morton A, Bond Pricing and the Term Structure of Interest Rates: A New Methodology, Econometrica 1992; 61:77-105. doi: 10.2307/2951677
Heath D, Jarrow R, Morton, Spindel M, Easier done than said, Risk 1992; 5(9): 77-80.
Hull J, White A, Pricing Interest-rate Derivative Securities, The Review of Financial Studies 1990; 3: 573-592. doi:10.1093/rfs/3.4.573
Hull JC, Sokol A, White A, Short rate joint-measure models, Risk 2014; October: 59-63.
Jamshidian F, LIBOR and Swap Market Models and Measures, Finance and Stochastics 1997; 1:293–330. doi:10.1007/s007800050026
Kahn R, Fixed income risk modelling. The Handbook of Fixed Income Securities, Third edition, edited by F. Fabozzi, 1991. p.1307-1319.
Mercurio F, Moraleda JM, An analytically tractable interest rate model with humped volatility. European Journal of Operational Research 2000; 120(1): 205-214. doi:10.1016/S0377-2217(98)00382-8
Moraleda JM, Vorst TC, Pricing American interest rate claims with humped volatility models, Journal of Banking & Finance 1997; 21(8): 1131-1157. doi:10.1016/S0378-4266(97)00019-8
Norman J, Real World Interest Rate Modelling with the BGM Model, SSRN working paper 2009; doi:10.2139/ssrn.1480174
Ross S, The recovery theorem. The Journal of Finance 2015; 70(2): 615-648. doi: 10.1111/jofi.12092
Stanton R, A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk, Journal of Finance 1997; 52: 1973–2002. doi:10.1111/j.1540-6261.1997.tb02748.x
van der Vlies M, Ignorance and Sophistication: the Impact of Heterogeneity on Mortgage Prepayments Doctoral dissertation, Universiteit van Amsterdam, 2016
Yasuoka T, LIBOR Market Model under the Real-world Measure, International Journal of Theoretical and Applied Finance 2013; 16(4):1350024(18 pages). doi: 10.1142/S0219024913500246
Yasuoka T, Interest-rate Simulation under the Real-world Measure within a Gaussian HJM Framework, Quantitative Finance Letters 2015; 3(1):10-16. doi: 10.1080/21649502.2014.995213
Yasuoka T, Correlations between the Market Price of Interest Rate Risk and Bond Yields. Journal of Reviews on Global Economics 2017; 6: 208-217. doi:10.6000/1929-7092.2017.06.19
Yasuoka T, Interest Rate Modeling for Risk Management: Market Price of Interest Rate Risk (second edition), Sharjah: Bentham, 2018.
Yasuoka T, Evaluating Credit Exposure of Interest Rate Derivatives under the Real-world Measure, J. of Risk Model Validation, to appear.
Copyright (c) 2018 Takashi Yasuoka
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Authors contributing to this journal agree to publish their articles under the Creative Commons Attribution-Noncommercial 4.0 International License, allowing third parties to share their work (copy, distribute, transmit) and to adapt it, under the condition that the authors are given credit, that the work is not used for commercial purposes, and that in the event of reuse or distribution, the terms of this license are made clear. With this license, the authors hold the copyright without restrictions and are allowed to retain publishing rights without restrictions as long as this journal is the original publisher of the articles.
